Polyphase reactive component measuring device



Aug. 28, 1951 A. .1. PETZINGER 2,565,824

POLYPHASE REACTIVE COMPONENT MEASURING DEVICE Filed Jan. 29, 1948 a: 254W V 7 4/bjW I INVENTOR JmroyeJPefzm aa;

ATTORNEY Patented Aug. 28, 1951 POLYPHASE REACTIVE COMPONENT MEASURING DEVICE Ambrose J. Petzinger, Fair Lawn, N. .I., assignor to Westinghouse Electric Corporation, East Pittsburgh; Pa., a corporation of Pennsylvania Application January 29, 1948, Serial No. 5,117

This invention relates to electrical measuring devices and it has particular relation to devices for measuring a reactive component of the power in a three-phase alternating-current system.

For measuring a reactive component of power in an alternating-current system, it has been the general practice to employ phase shifters which in some cases are known as phase transformers or. reactive component compensatorslv The prior art practice is set forth in the Electrical Metermens Handbook, published inv 1940 by the Edison Electric Institute of New York City, th edition. The reactive component desiredmay be instantaneous reactive power, reactive power demand or integrated reactive power, Another form of reactive power meter is disclosed in the Lenehan Patent,l,'132,687.

In accordance with the invention, devicesfor measuring a reactive component of a three-phase system are energized directly from the associated three-phase system. By a novel selection of voltages and currents supplied to a suitable measuring device, the invention eliminates the phase shifters formerly employed for such measurements. 7

It is, therefore, an object of the invention to provide an improved device for measuring a reactive component of a three-phase alternatingcurrent electrical system.

It is a further object of the invention to provide a measuring device for measuring a reactive component of a three-phase alternating-current electrical system wherein the measuring device is energized directly from the associated system without necessitating the utilization of phase shifters.

Other objects of the invention will be apparent from the following description taken in conjunction with the accompanying drawing, in which:

Figure 1 is a schematic view of an alternatingcurrent system embodying the invention;

Figure 1A is a vector diagram showing voltage relationships for the system of Fig. l; and

Figs. 2 and 3 are schematic views showing alternating-current systems embodying modified forms of the invention.

The invention is applicable to various polyphase alternating-current electrical systems operating at any desired frequency. For the purpose of illustration, the invention will be discussed with reference to three of the systems commonly encountered in the art, namely (1) the three-wire three-phase alternating-current system, (2) the four-wire'star-connected threephase alternating-current system, and. (8) the 9 Claims. (01. 171 34) four-wire delta-connected alternating-current system. It will be assumed for the purpose of discussion that the systems operate at a frequency of cycles per second. I, H

Referring to the drawing, Fig. 1 shows a threewire three-phase alternating-current electrical system employing phase-conductors I, Z and 3. Although, as well understood in the art, the system may be energized from either deltaor star-connected windings, it will be assumed that the system is energized from three delta-connected windings a, b and c which constitute the secondary windings of a conventional polyphase power transformer.

For the purpose of discussing the invention, a conventional system of notation will be employed. The phase-"conductors I, 2 and 3 carry respectively currents I1, I2 and Is. The voltages between the phase conductors are represented by the symbol E accompanied by a subscript formed by the numerals of the phase conductors between which the voltage is taken. For example, the voltage E21 represents the voltage between the phase conductors 2 and I. A reversal of the numerals in thesubscri-pt, indicates a reversal in phase of the voltage represented thereby. As shown in Fig. 1A, a conventional counterclockwise rotation of thevectors representing the three phase voltages is assumed and the phase conductors have been numbered in accordance with such phase rotation. I

In order to measure a reactive component of the system shown in Fig. 1, a two and one-half element meter (also known as a two-element split-coil meter) H is employed. Such a meter is well known in the art and includes two elements I3 and I5. The upper element I3 has a voltage winding I3a and two current windings I31) and I30. The lower element I5 has a voltage winding I5a, and two current windings I51) and I50, The voltage winding I5a and its associated current windings I5b and I50 operate when energized to establish a shifting magnetic field. Similarly, the voltage winding Ba and associated current windings I3b and I30 cooperate when energized to establish a second shifting magnetic field. As well understood in the art, a common electroconductive armature or two mechanically connected armatures may have portions disposed in the two shifting magnetic fields for rotation in response to torques developed by the fields acting on the armatures.

For energizing the meter I5, a voltage transformer IT has its primary connected for energization by the voltage E23. A voltage transformer have their primary windings respectively in the,

phase conductors I and 3 for supplying energy to the current windings of the meter l5.

The operation of the system illustrated in Fig.

1 may be understood more clearly from a'brief consideration of the underlying theory. From Blondels theorem, the real power .P :flowing in the phase conductors I, 2 and 3 is represented by the following expression:

Inasmuch as the reactive power Q is in quadra- 'turewith thereal power P, the reactive power may be obtained 'by rotating the voltages of Equation '1 by 90. For measuring leadingreactive power, the voltages should be rotated counterclockwise 90 as represented by the vector operator-1i. (It willbe understood'that the voltages and currents herein discussed are vector quantities.) powenfthe voltages should be rotated 90 in the opposite direction as indicated by the operator (-7) Since in mostcases it is desired to measure lagging power, the reactive power Q may be represented by the following expression:

The'invention assumes-thatthe phase or 'line voltages always remain balanced. In modern "distribution systems, the unbalance of the volt- L yg .an'dlmaking" the indicated substitutions, Equation 2' may be rewritten asfollows:

-Equation '3 may :be simplified by making the sub- .stitution E31 E32+E21 This substitution results in'ithe following expression:

'For measuring lagging reactive A study of Equation 4 indicates that this equation may be employed as a basis for measuring reactive power without employing phase shifters. For example, if the voltage winding [3a of the meter is energized in accordance with the voltage E21, voltage winding l5a is energized in accordance with the voltage E 23, the :current winding I30 is energized'in accordance with 212, the current windings |3b and l5c are energized in accordance with the current I1 and the current winding [5b is energized in accordance with the currentIz, the meter [5 has an output dependent on reactivepower. It will be understood that the polarities of the connections are selected to sat- .isfy Equation 4.

Some simplification of Equation 4 may be obtained by making the substitution:

I1=I2I3 to produce the following equation:

The expressions are full equivalents. However, the latter facilitates the utilization of similar equipment throughout -for the reason that it eliminates the multiplying factor for the current I2.

The meter ll of "Fig. 1 'is illustrated as connected in accordance with the requirements of Equation '5. It will be noted that the current winding -l3b is connectedin series with the secondary winding of the current transformer 23 for energization in accordance With the current 13; The current winding l5bo'f'the meter is connected in series with the secondary winding of the transformerl I for energization in accordance with the-current I1. 'Inasmuch asthe current I: is equal'to -(I1 -i-I3) ,the currents from the windings I3b-and [5b are conducted to-acommon terminal 25 from which a current equal in value to 12 flows through the windings [3c and I50 in series to the -right-'-hand terminals of the current transformer secondary windings.

From the foregoing discussion, it will be apparent that'when the meter H is connected as illustrated in Fig. 1, the meter armature will be actuated in accordance with the reactive power of thevthree-phase three-wireelectrical system. The meter mayinclude conventional integrating registers, demand indicators, and recording mechanism, as desired.

The factor wire alternating-current system .of Fig. "2, the

.three. conductors l,2 and 3 are connected to the terminals of three star-connected windings a",

-point of the star-connected windings is connected to a neutral conductor 0 to direct a current I0 through the neutral conductor. A twoelement meter 21 is employed which includes elements 29 and 3|. The element 29 has a voltage winding 29a and two current windings 29b and 290. The element 3| has a voltage winding 3m and two current windings 3H) and 310. .The V voltage windings 29a and 3la are connected through voltage transformers-33 and respectively for energization in accordance with the voltages E30 and E10. If the meter voltage windings can be designed conveniently for line voltages, the voltage transformers need not be employed. The current transformers 2| and 23 are again employed but an additional transformer 22 has its primary winding included in the conductor 2.

The connections of the meter 21 in Fig. 2 may be understood from the following discussion. By inspection of Fig. 2, it will be observed that reactive power Q of the system may be represented by the following expressions:

By substituting E02= (E01+E03) Equation 7 becomes Equation 8 may be simplified by substituting I1+I2+I3=-Io to produce the following expression In order to measure reactive power in accordance with Equation 9, the meter 21 must properly weight the currents. The secondary windings of the current transformers are connected in star and the neutral connection of the windings is connected to the windings 29c and 310 to energize these windings in accordance with the current I0. The current winding 29b is connected to the secondary winding of the current transformer 2! for energization in accordance with the current I1. A current winding 3Ib is connected to the secondary winding of the current transformer 23 for energization in accordance with the current 13. The output of the current transformer 22 is combined with the currents passing through the windings 29b and 31b to produce a current proportional to the neutral current In for energizing the windings 31c and 290.

The desired weighting of the currents could be obtained by providing separate transformers for the currents 13, I0 and I1 and then adjusting the turn ratios of the transformers to provide the desired weighting. To permit the utilization of similar current transformers, the desired weighting is obtained in Fig. 2 by providing the current windings 29b and MD with three times the number of turns employed for the windings 29c and 3lc. .When the meter 21 of Fig. 2 is connected as illustrated, it may be calibrated to read directly the reactive power of the associated electrical system. The factor is incorporated in the manner, discussed with reference to Fig. 1.

In Fig. 3, the conductors l, 2, 3 and 0 again are employed for providing a three-phase fourwire service. These conductors are connected to delta-connected secondary windings a", b and c" of a power transformer. It will be noted that the winding a has a center tap to which the neutral conductor 0 is connected.

For measuring a reactive component of the alternating current circuit, a two-element meter 3": is provided which includes an upper element 39 and a lower element 4|. The upper element of the meter comprises a voltage winding 39a and two current windings 39b and 390. The lower element 4| includes avoltage winding Ma and one current winding 41b. The voltage windings 39a and Ma are connected respectively through voltage transformers 43 and 45 for energization in accordance with voltages E03 and E12. Since the voltages E10 and E02 are each equal to one-half the voltage E12, either of the voltages Emand E02 may be employed for energizing the transformer 45 if the transformation ratio of the transformer is selected to provide the desired output voltage. This is indicated in Fig. 3 by a removable link 45a which is employed to connect one terminal of the primary winding to the conductor2. If desired, this link may be transferred to an intermediate tap 45?) on the primary winding to connect the intermediate tap to the conductor I}. If the meter voltage windings can be designed conveniently for energization directly by the desired line voltages, the voltage transformers need not be employed. The current transformers 21, 22 and 23 again are employed with the conductors I, 2 and 3, respectively.

The desired connections of the meter 21 may be understood from a development of an expression for reactive power. In accordance with Blondels theorem, the real power P for the circuit shown in Fig. 3 may be expressed as follows:

I I P=E12(32--*2-) a0 a In order to obtain the reactive power, the voltages, Equation 10, may be replaced by corresponding quadrature voltages as follows:

To satisfy this equation, the current windings 39b, 39c and Mt are connected for energization respectively across the secondary windings of the current transformers 2 l, 22 and 23. The desired weighting represented by the factor 22and 23 have equal transformation ratios. The

desired weighting is obtained 'by providing the current winding '4 ID with ciate a1ternating-current circuit. The factor may be incorporated :in ,the .manner discussed previouslyiorzthe corresponding-factor of Fig. 1. Although :the invention has been described .With reference to-icertain ispecific embodiments thereof, numerous modifications falling within the spirit and scope of the invention are possi- I claim as my invention:

;1. Inga device for measuring areactive component of a three-phase alternating-current system having :three phase-conductors :numbered in the order of conventional phase rotation 'l, 2, 3 carrying currents I1, 12 and I3 respectively, said system having a voltage E12 between the conductors! andlandhaving a voltage E23 between the conductors 52 and 3,ea multi-relement meter having watt-responsive elements, and means connecting the elements to the-system rfor energization respectively in accordance with the expressions E12(I3I2) and E2:( I1,-I2) to provide a meter =resp.onse proportional to the expression said means comprising a pair of current transformers, connections-for energizing the elements from said, current transformers in accordance withthe respective currents supplied to-the current transformers, and connections for energizing said elements from said current'transformers in accordance with'the vector resultant of the respective currents supplied-to thecurrenttransformers.

2, A device as-claimedin claim 1, wherein a first one of said z-watt-responsiveelements has a voltage winding connected for energization in acccrdance with the voltage between the conductors i and 2, and a pair of current windings connected :for energization respectively in accordance with thecurrents in the conductors 2 and 3, and wherein a second one of the watt-responsive elements has a voltage winding connected for energization in accordance with the voltages between the conductors 2 and '3, and a pair of current windings connected for'energizationrespectively in accordance with'the currents in the :conductors l and 2.

3. In combination with a three-phase, -fo urwire, star-connected alternating-current system having three phase-conductors numbered in the order of conventional phase rotation I, 2, 3 carrying currents I1, 12 and I3 and a neutral conductor carrying a current I said system having voltages Em and E30 between thephase-conductors for energization respectively-inaccordance with the expression E01('3I3+J0) and E03(3I1+I0) to provide a meter response proportional to the expression .Eo1(3'13 +10) VE03 311 +10) 4. A device as claimed in claim 3, wherein a first one of said elements has a voltage winding connected for energization in accordance with the voltage between the conductor I and the neutral conductor, and a pair of current windings connected 'for energization respectively in accordance with the currents in the conductor 3 and in the neutral conductor weighted in accordance with the expression (313-1-10), and wherein -a second one. of the elements has a voltage winding connected for energization in accordance with the voltage between the conductor '3 and the neutral conductor, and a pair of current windings connected for energization respectively in accordance with the currents in the conductor l and the neutral conductor weighted in accordance with the expression (311+Io) 5. In a device for measuring a reactive component of a three-phase, four-wire, delta-connected alternatingecurrent system having three phaseconductors numbered in theorder of conventional phaserotation l,;'2,*"3 carrying currents I1, 12 and I3 respectively and having a neutral conductor providing with the conductors I, 2 a three-wire single-phase service, said system having a voltage E03 between the neutral conductor and the phase conductor 3, and said system having a voltage E12 between the phase conductors [and :2, a multi-element meter having watt-responsive elements, and means connecting the elements to the system for energization respectively in accordance with theexpressions E03(I1I2) and gain to provide a meter response proportional to the expression 6. A device as claimed in claim 5 wherein a first one of said elements has a voltage winding connected for energization in accordance with said voltage E03, and a pair of current windings connected for energization respectively in accordance with currents in the conductors I and 2, and wherein a second one of the-elements has a voltage winding connected for energizationin accordance with the voltage E12, and a current winding connected for energization in accordance with the current 13.

'7. Ina device for measuring a reactive component of athree-phase, four-wire system, a twoeIement,Watt-responsive meter comprising a first element having a voltage winding and first and second current windings cooperating with the voltage winding, and a second element having a voltage-winding and first and second current windings cooperating with the last-mentioned voltage vvinding rneans connecting the first current --Wi-ndings of the elements for energiza- -tionfrom a source-of energy,separate connection nent of a thYEE-DhflSGyfOllIf-Wile system, a two- --element, watt-responsive meter comprising a first element having a voltage winding and first and second current windings cooperating with the voltage winding, and a second element having a voltage winding and a current winding cooperating with the last-named voltage winding, means connecting the windings for energization from sources of voltages and current, said windings and connecting means being weighted to provide ratios of input to the connecting means to output from the elements which bear the relationship of 2 to 3 for the first element and associated connecting ,means relative to the second element and associated connecting means.

9. In a device for measuring a reactive component of a three-phase, four wire, alternating-current system having three phase conductors numbered in the order of conventional phase rotation I, 2, 3 carrying currents I1, 12, I3 and a neutral conductor carrying a current Io, a multi-element meter having two watt-responsive elements each including voltage and current windings, and translating means responsive to a function of the voltage and current applied to the windings of each of the elements, connections for energizing a voltage winding of a first one 0! said elements in accordance with the phase and magnitude of the voltage between the neutral conductor and a first one of said phase conductors, connections for energizing a voltage winding of a second one of said elements in accordance with the phase and magnitude of the voltage between the neutral conductor and a second one of the phase conductors, and connections for energizing the current windings from said phase conductors to provide a response by the translating means which is dependent on the reactive power of the system.

AMBROSE J. PETZINGER.

REFERENCES CITED The following references are of record'in the file of this patent:

UNITED STATES PATENTS Number Name Date 1,281,399 Landis Oct. 15, 1918 1,580,408 Cheetham Apr. 13, 1926 

